CIHM 
Microfiche 
Series 
(i\/lonographs) 


ICiVIH 

Collection  de 
microfiches 
(monographies) 


Canadian  Institute  or  Historical  Microreproductions  /  Institut  canadien  de  microreproductions  historiques 


©2000 


Technical  and  Bibliographic  Notes  /  Notes  techniques  et  bibliographiques 


The  Institute  has  attempted  to  obtain  the  best  original 
copy  available  for  filming.  Features  of  this  copy  which 
may  be  bibliographically  unique,  which  may  alter  any  of 
the  images  in  the  reproduction,  or  which  may 
significantly  change  the  usual  method  of  filming  are 
checked  below. 


Coloured  covers  / 
Couverture  de  couleur 


r~7|    Covers  damaged  / 


Couverture  endommag^e 


□    Covers  restored  and/or  laminated  / 
Couverture  restaur^e  et/ou  pellicul^e 

Cover  title  missing  /  Le  titre  de  couverture  manque 

I I   Coloured  maps  /  Caries  g6ogr^phiques  en  couleur 

□    Coloured  ink  (i.e.  other  than  blue  or  black)  / 
Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 

□    Coloured  plates  and/or  illustrations  / 
Planches  et/ou  illustrations  en  couleur 

I      I    Bound  with  other  material  / 


D 


D 


Reli6  avec  d'autres  documents 

Only  edition  available  / 
Seule  Edition  disponible 


n  Tight  binding  may  cause  shadows  or  distortion  along 
interior  margin  /  La  reliure  serr^e  peut  causer  de 
I'ombre  ou  de  la  distorsion  le  long  de  la  marge 
int^rieure. 


Blank  leaves  added  during  restorations  may  appear 
within  the  text.  Whenever  possible,  these  have  been 
omitted  from  filming  /  II  se  peut  que  certaines  pages 
blanches  ajout6es  lors  d'une  restauration 
apparaissent  dans  le  texte,  mais,  lorsque  cela  etait 
possible,  ces  pages  n'ont  pas  et6  film^es. 


L'Institut  a  microfilme  le  meilleur  exemplaire  qu'il  lui  a 
ete  possible  de  se  procurer.  Les  details  de  cet  exem- 
plaire qui  sont  peut-etre  uniques  du  point  de  vue  bibii- 
ographique,  qui  peuvent  modifier  une  image  reproduile. 
ou  qui  peuvent  exiger  une  modification  dans  la  metho- 
de  normale  de  filmage  sont  indiques  ci-dessous. 


D 


Coloured  pages  /  Pages  de  couleur 
l/\    Pages  damaged  /  Pages  endommagees 


D 


Pages  restored  and/or  laminated  / 
Pages  restaurees  et/ou  pelliculees 

y|    Pages  discoloured,  stained  or  foxed  / 
i_J    Pages  d^colorees,  tachetees  ou  piqu6es 

I    Pages  detached  /  Pages  detachees 

Showthrough  /  Transparence 

I      I   Quality  of  print  varies  / 


D 
D 


D 


Quality  in^gate  de  I'impression 

Includes  supplementary  material  / 
Comprend  du  materiel  suppl6mentaire 

Pages  wholly  or  partially  obscured  by  errata  slips, 
tissues,  etc.,  have  been  refilmed  to  ensure  the  best 
possible  image  /  Les  pages  totalement  ou 
partiellement  obscurcies  par  un  feuillel  d'errata,  une 
pelure,  etc.,  ont  6t6  filmees  a  nouveau  de  fa?on  a 
obtenir  la  meilleure  image  possible. 

Opposing  pages  with  varying  colouration  or 
discolourations  are  filmed  twice  to  ensure  the  best 
possible  image  /  Les  pages  s'opposant  ayant  des 
colorations  vanables  ou  des  decolorations  sont 
filmees  deux  fois  afin  d'obtenir  la  meilleure  image 
possible. 


Additional  comments  / 
Commentaires  suppl^mentaires: 


Pagination  is  as  follows:  p.  274-277. 

La  pagination  est  comme  suit:  p.  274-277, 


Thit  item  it  filmed  at  the  reduction  ratio  checked  below  / 

Ce  document  eat  filmi  au  taux  de  rMuction  indiqui  ci-desioua. 


lOx 

14x 

18x 

22x 

26x 

30x 

/ 

12x 

16x 

20x 

24x 

2SX 

32x 

The  copy  filmed  h«r«  has  b««n  r«predue«d  thanka 
to  tha  ganarosity  of: 

Gerstein  Science  Information  Centre 
University  of  Toronto 

Tha  imagas  appaaring  hera  ara  tha  bast  quality 
possibia  considaring  tha  condition  and  lagibii'ty 
of  tha  original  copy  and  in  kaaping  with  tha 
filming  contract  spacificationa. 


L'axamplaira  film*  fut  raproduit  grica  A  la 
ginArosit*  da: 

Geri>tein  Science  Information  Centre 
University  of  Toronto 

Las  imaga*  tuivantas  ont  At*  raproduitas  avac  la 
plus  grand  soin.  compta  tanu  da  la  condition  at 
da  la  nattat*  da  l'axamplaira  film*,  at  an 
conformity  avac  las  conditions  du  contrat  da 
filmaga. 


P"  i-*i 


Original  copias  in  printad  papar  covars  ara  filmad 
beginning  with  tha  front  covar  and  anding  en 
tha  last  paga  with  a  printad  or  illustratad  improa- 
sion,  or  tha  back  covar  whan  appropriata.  All 
othar  original  copiaa  ara  filmad  iMginning  on  tha 
first  paga  with  a  printad  or  illustratad  impraa- 
sion,  and  anding  on  tha  laat  paga  with  a  printed 
or  illuatratad  impraaaion. 


Laa  axamplairaa  originaux  dont  la  couvanura  tn 
papiar  aat  impHmAa  sont  filmte  an  commancant 
par  la  pramiar  plat  at  an  tarminant  soit  par  la 
darnlAra  paga  qui  comporta  una  amprainte 
d'imprassion  ou  d'illustration,  soit  par  la  second 
plat,  salon  la  caa.  Tous  lea  autras  axemplairas 
originaux  sont  film*s  an  commanpant  par  la 
pramiire  paga  qui  comporta  una  ampreinte 
d'impreasion  ou  d'illustration  at  an  tarminant  par 
la  darniire  page  qui  comporte  une  telle 
empreinte. 


The  last  recorded  frame  on  each  microfiche 
shell  contain  tha  symbol  -^  (meening  "CON- 
TINUED"), or  the  symbol  ▼  (meening  "END"), 
whichever  applies. 


Un  dee  symboles  suivents  tppsraitra  sur  la 
derniire  Imege  de  cheque  microfiche,  selon  Is 
cas:  la  symbols  — »>  signifie  "A  SUIVRE",  le 
symbols  ▼  signifie  "FIN". 


Mapa.  plates,  cherts,  etc.,  may  be  filmed  et 
different  reduction  ratios.  Those  too  large  tu  be 
entirely  included  in  one  exposure  ere  filmed 
beginning  in  the  upper  left  hend  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  aa 
required.  The  following  diegrems  illustrate  the 
method: 


Lee  cartas,  planches,  tableeux.  etc..  peuvent  itre 
filmte  i  das  taux  de  riduction  diffirents. 
Lorsque  le  document  est  trop  grend  pour  Atre 
raproduit  en  un  seul  cliche,  il  est  film*  e  psrtlr 
de  I'engle  supArieur  gauche,  de  gauche  i  droite. 
et  de  heut  en  bea,  en  prenent  le  nombre 
d'imoges  nicessaire.  Lea  diagrammas  suivents 
illustrent  le  mtthode. 


1  2  3 


1 

2 

3 

4 

5 

6 

MKIOCOPV   ItSmUTION   TBI  CHART 

(ANSI  and  ISO  TEST  CHART  No    2| 


_^  ^jPPLIED  IIVMGE 

^BV  '653   Foil   Ma;'    Slre,i 

P^S  ''ocMester,    f^^»   Yci,         U609       dS 

^S  ("6)   482  -  030O  -  Pnont 

^S  <"6)  J«8  -  6989  -  to. 


Wll  Pmiini'^^U  <]  i¥  '^ii^¥^- 


^     Repnnleil  from  the  Ast«oihysicai    Joiunal,  Vol.  XXVIII,  No.  4.  N-vrmber  1908 


^^-^\' 
^^«^      ^ 


THE  ORBIT  OF  i  ORIONIS 


tZJ 

■  -t 
•o 


J.  S.  PLASKKTT 


I'RINTKI)   AT    THK    UNIVKRSIIV    <1F   CHK  Alio    I'RKSS 


(^A'^^n  '5^V 


K^iPS'^;- 


'  ■<'. 


M 


TMK   OK  HIT   OF  <  (>A7()A7.S' 

lis  J  ■'  ri.\>Ki  I  I 

Acting  on  a  >iipm>ti()n  kindly  made  lo  nic  li\  Dr.  Si  lili -iiij^i  r.  a 
Icast-sijiiari's  solution  has  lutn  apiilitd  'i  >  tin-  clctntni-  of  the  orhii  of  i 
Oriotiis  Tvcvnih  jmhlislu'il  in  ilii>  JouriuiL'  .\>  |>rtlirninar\  tltnirnt> 
thosi"  (Iciirmincd  in  the  ahovi-  pajnr  wtU'  lakiii.  and  tlir  ii^  piair- 
wtTr  grouju'd  into  jO  normal  plan^.  the  -inn-  a^  htlorr  txcciit  for 
some  minor  chan;4cs  intro<iuii(l  hy  a  con^i  ;i  ni  ss-tcni  of  ucii^iitinL;. 
An  i'|)hcmt'ris  havinf^  bi'tn  comiiuU'd  iv  .—  -  '  mcni^,  ilu  ( ihIVi- 
cienis  of  the  unknowns  in  ilir  ohsir\a''  is  wtn'  laK  ulaicd 

from  the  formulai-  of  I.chmann  Filhi'-'  for  .  .  o'  du  •>(■  j.Lk  rs.  TIk- 
piTiod  was  considered  as  very  t  losdy  .!  ti  rniincd  hy  ilic  imthod 
previously   used   and   a  eornilion  eon>idered    iinneei-.~ar\. 

From  the  oh'-ervation  e(|uations  wire  fornnd  the  normal  e(iua- 
tions  below,  tlu-  following  factor^  l)iinL;  iiiirixiiHed  for  iiomo^eiieity: 


.V 

=8a: 

V 

=  A>=i 

I2&; 

: 

Ktu,  = 

128.,. 

u- 

Am 

fii     S,? 

4f)rt/ 

V 

=  8y 

NOKMAI.    ri.UAriOVS 

+  44.()68.v  —   2Q.522V   4-    v.^---      +   0-.^-7"      ~i4.2()i;'   -f   cjS. 606=0 
+  228.507y  — 41  S<)();      -fh^.d^o/i      *- ^(j  oSijr   --'44.074^-0 

+  51.724:     - -,s  4.ii"       ,vVg-"<;;'  -  ,vi  44-'    o 

+  76  Q4o;(      +25  424;'   -  56  ,^7,v-o 
4-95.000;'   —    i5.S'X>'0 

The  solution  of  these  e(|uatioi-  L'ave  tiie  following  corrected  ele- 
ments: 

'  A^lrofthyuiiil  Jiniriut!,  27.  ;- 2,  iijcS. 
t  Astri'*ionji\cbe  Wtt  Itrichtrii.  136.  17.  isijj, 

-^74 


Tin:  Oh'lUI    Oh   I  DRliKM.S 


275 


V 

M 


K 
e 


y 

Period 
a  sin  t 


rrilmmi.iry  f..rriilni 

IlJ  o  loq  c)2 

0.75  0,7552 

110°  I1.^?3I 

i.()4  (lays  1  (wi  days 

+  20.7  km  +  J  1.34  km 

29. 1.0  (lays  20.136  days 

29,680,000  kill  28,867,000  km 

A  comparixm  of  thr  n  !diial>  ohlaimd  from  an  ipht-mfris  and 
from  siihstilution  in  tlie  obMTvation  tciuations  ^howid  somr  diltiT- 
cnccs  of  oviT  a  kilomcti-r  and  a  sicond  sohuion  was  mrcssary.  For 
l)ri-liminary  flrmcnls  thosi-  olitainol  in  the  first  -oluiion.  fxcqit  T, 
vvhicl)  was  incrt-a^'d  to  2.01  days,  witi-  umiI.  'liif  change  in  T 
was  dm-  to  a  lu-ttir  aj^nrmunt  tlurihy  prciuci'd  in  tlu'  ivsidual>. 
Using  tin-  samo  Mib.-tituiions  for  lionu)gcmii>  tluri'  risull  ihr  normal 
c(|uations 

+45.OSH.V   -  2S.047.V    +   2.576s    +  o  726H    -14.660:'    -     o  --1=0 

4-266.()()4.v    -45.686:     +65.208/<     +4^  697:'     +II7-;    2=0 

+  50.3723    -48.247«    -33  053:'    -   70.762=0 

+  64.085X    +jj.897f    +  95.820=0 

+  95.000:'    +   34.800=0 

Tlu'ir  solution  giv("^  for  linal  I'liimnts  tlu'  following: 


A' 

e 


y 

Period 


109.90     +  I    100  km 

o.754,S±     0046 
ii3?28     ±1:083 

1  993   ±    .022  days^Juliun  l>.i\  2,417,387.993 

+  21.34     io.856km 

29. 136  days 
28,()07,ooo  km 


.\n  t'plienu'ris  computi'd  from  llu'sc  ek'm(.'nt>  >liows  that  ^pvi' 
has  been  reduced  from  2>)nA  to  -'i'"^'-  the  probable  error  of  an  obser- 
vation of  unit  weight  becoming  ±().8S  km,  whili'  the  probable  error> 
of  the  element^  become  those  given  above.  The  cluinges  from  the 
first  solution  arc  very  small  but  the  agreement  between  thi'  ri'- 
siduals  is  now  satisfactory.  The  \el.Kity-curve  corresponding  to 
the  linal  elements  is  given  in  the  accompanying  figure,  with  the 
IK)^itions  of  the  normal  i)laces  as  small  circles.     .\  comparison  of 


a76 


J.  S.  PLASKHTT 


int.  OHUJl   OF  I  ilRUfSIS 


277 


ihis  with  ilu-  previous  ''Rurr  shows  that  thi-  gtncral  trend  of  the 
()^J^^T\ati^)n>  is  more  cl()>cly  followed.  The  j)rol)ability  of  a  seton<i- 
;'rv  disiurhance  seems  somewhat  le»  than  with  the  original  ele- 
ments, atid  this  is  ftinhef  lessened  !>>  a  knowiedj^e  of  the  fact  that 
the  normal  places  with  the  highest  resi<hials  contain  always  one  or 
more  observations  with  the  universal  s|K'Ctrosco[)e  where  the  tem- 
[lerature  control  was  p(K)r  and  the  siH-ctra  contained  only  two  meas- 
urable lines. 

The  restdt  of  this  comjuitalion  seems  to  justify  Dr.  SchlesinRer's 
contention  that,  ■  ven  in  tin-  case  of  spectra  in  which  accurate  meas- 
urement is  imjHi-sible,  the  least-scjua'-vs  solution  will  jjive  the  best 
determination  of  the  elements  of  a  bin.i.-y  orbit. 

DoUINIOS    l)BSK.RV\Tl)RV,    OrfAXVA 

July  190.S 


